Do you consider fantasy elements supernatural or are you just looking for psychological horror? If so recommend The Alienist and The Angel of Darkness by Caleb Carr, the Hannibal books by Thomas Harris and as mentioned above, The Blue Rose Trilogy by Peter Straub.

H.P. Lovecraft was an atheist who didn't believe in the supernatural, Thus, the stories and novels which centre around the Cthulhu Mythos and the Necromonicon of the Mad Arab Abdul Alhazred represent his best work. He was trying to scare people who didn't believe in the supernatural.

One of the most horrifying stories I have ever read in my life is the short story by William Faulkner, "A Rose for Emily".

Indeed, most Lovecraft stories involve either aliens with hidden agendas outside human comprehension or pure psychological horror based on first person account by an unreliable narrator (mad). Supernatural only exists in the minds of those who believe it and if the narrator says so, so it is written...

Its astonishing how many well read people I talk to who have no clue about anything Lovecraft. Definitely not for everyone though, a big part of Lovecrafts work is what is not said or explained. Also not everyone likes an uncertain ending.

A Rose for Emily is one of the very few stories I enjoyed from school.

Well, 'no supernatural' pretty much eliminates the entire genre, since horror usually makes use of fear of the unknown. Otherwise it's generally labeled a "thriller." There's exceptions, but they're exceptions. Serial killer stories are probably as close as it gets.

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Originally Posted by siraks

The Monstrumologist

Amazing book, and technically it isn't a tale of the supernatural, since the creatures are just a lesser-known species of predator, at least within the narrative. The creatures are rather fantastical, though.